Question 1
Write True or False and justify your answer : ABCD is a parallelogram and X is the mid - point of AB. If ar (AXCD) = 24cm2, then ar (ABC) = 24cm2
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Solution
False.
Given, ABCD is a parallelogram and ar (AXCD) = 24cm2 Let area of the parallelogram ABCD is 2y cm2.
Join AC.
We know that, diagonal divides the area of parallelogram in two equal areas. ∴ar (ABC) = ar (ACD) = y So, ar (ACX) = ar (BCX) [since, x is median in △ABC] =12ar(ABC)=12y
Now, ar (AXCD) = ar (ADC) + ar (ACX) 24=y+y2 ⇒24=3y2 ⇒ar(ΔABC)=16cm2 Therefore, given statement is false.